Fri Oct 19, 2012
60 Evans Hall, 4:10–6 PM
Thomas Scanlon (UC Berkeley)
A Logic for General Differential Equations
Differential and difference equations have been studied from the point of view of model theory through the theories of model-complete differential and difference fields. The known theorems are similar, but the theories have been developed in parallel. I will report on joint work with Rahim Moosa in which we propose a general theory of D-fields, proving the existence of model companions, describing the definable sets, and establishing the fine-structural Zilber trichotomy principle uniformly. Our theory also grounds a general Galois theory for difference/differential equations and provides a rigorous framework for understanding the confluence from difference to differential equations.